Reentrant quantum phase transition in double-well optical lattices

We study the quantum phases of bosons confined to a combined potential of a one-dimensional double-well optical lattice and a parabolic trap (two-legged ladders). We apply the time-evolving block decimation method to the corresponding ladders described by a two-legged Bose-Hubbard model. In the absence of a parabolic trap, the system of bosons in the double-well optical lattice exhibits a reentrant quantum phase transition between Mott insulator and superfluid phases at unit filling as the tilt of the double wells is increased. We show that this reentrant phase transition still occurs in the presence of a parabolic trap, and we suggest that it can be detected experimentally by measuring matter-wave interference patterns.

Figure 1

(Color online) Schematic double-well lattice potentials in the $xz$ plane $(y=0)$ for $\alpha =0.2$, $V_{\mathrm{in}}=20E_R$, $V_{\mathrm{z}}=5E_R$, showing the existence of isolated two-legged ladders. In (a) double wells are symmetric $(\theta =0\mathrm{radian})$, while in (b) double wells are tilted $(\theta =0.2\mathrm{radian})$.

Figure 2

(Color online) Results at three values of $\lambda ∕U$: 0 (a) and (d), 1 (b) and (e), and 2 (c) and (f). In the left three figures, we show the phase diagrams of the homogeneous system in the $(\mu ∕U,t_{\parallel }∕U)$ plane for $t_{\perp }=0.1U$, which have been calculated by means of the infinite-size version of the TEBD method. In the right three figures, the local number of bosons at the $j$th double well ${\overline{n}}_j$ (black squares), that at the $j$th left well $n_{j,L}$ (green diamonds), that at the $j$th right well $n_{j,R}$ (red triangles), and the fluctuation ${\sigma }_j$ of ${\overline{n}}_j$ (blue stars) are shown. Notice that in (d) the diamonds are completely overlapped with the triangles since $n_{j,L}$ and $n_{j,R}$ take the same value at $\lambda =0$. The dashed lines in the phase diagrams represent the values of the local chemical potential and $t_{\parallel }$ realized in the right figures. The upper (lower) end of the dashed lines corresponds to the center (edges) of the trapped gas.

Figure 3

(Color online) Density profile ${\overline{n}}_j$ as a function of $\lambda ∕U$. All the other parameters are fixed as $N=98$, $L=85$, $t_{\parallel }∕U=0.05$, $t_{\perp }∕U=0.1$, and $\Omega ∕U=0.001$.

Figure 4

(Color online) (a) Quasimomentum distribution $S\left(k\right)$ as a function of $\lambda ∕U$. (b) Visibility $V$ (black squares) and center density ${\overline{n}}_{j=0}$ (red triangles) as functions of $\lambda ∕U$.

Figure 5

(Color online) (a) Local coherence between the left and right wells $⟨a_{j,L}^{†}{a}_{j,R}⟩$ for $\lambda ∕U=0$ (black squares), $\lambda ∕U=1$ (red diamonds), and $\lambda ∕U=2$ (blue triangles). (b) Total coherence $C$ versus $\lambda ∕U$.